Satellite attitude system active fault-tolerant control method based on observer under dynamic interference

Abstract

The invention discloses an observer-based satellite attitude system active fault-tolerant control method under dynamic interference, which comprises the following steps of: firstly, establishing a mathematical model of a satellite attitude system by considering external interference, actuator fault and model uncertainty, and further designing a nonlinear interference observer to estimate the external interference in real time; meanwhile, an actuator fault is dynamically estimated through a fault estimator, and an adaptive law is constructed to carry out approximation on uncertainty of a system model; and designing an anti-interference fault-tolerant controller according to a satellite attitude system model in combination with an observer, an estimator, an adaptive law and a system state to realize attitude control of the satellite. According to the method, under the action of various factors, the stability of the system of the satellite can be kept, interference factors can be accurately compensated, good robustness and practicability are achieved, and the anti-interference capability of the satellite is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of satellite attitude control technology, specifically relating to an active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances. Background Technology

[0002] Recent breakthroughs in aerospace technology have epoch-making strategic significance for the evolution of human civilization, and their innovative achievements have opened up entirely new dimensions for human technological development. However, in the complex space environment, various uncertain external disturbances and potential satellite malfunctions pose extremely severe challenges to satellite attitude control. The main difficulty lies in designing control strategies for satellites under conditions of multiple uncertainties and energy constraints.

[0003] Many scholars both domestically and internationally have conducted research on satellite attitude system control. However, most studies focus on the influence of a single disturbance factor, neglecting the simultaneous impact of multiple factors such as external disturbances, actuator failures, and model uncertainties. In the complex space environment, with its various external disturbances, the key challenge is maintaining satellite stability under the influence of multiple uncertainties. Existing methods still have significant room for improvement in achieving high-precision and robust control. To address these issues, a novel fault-tolerant control method for satellite attitude systems needs to be developed. Summary of the Invention

[0004] Purpose of the invention: In order to overcome the shortcomings of existing satellite attitude system control methods in dealing with multiple disturbance factors, this invention proposes an observer-based active fault-tolerant control method for satellite attitude systems under dynamic disturbances. It uses an observer and an estimator to estimate external disturbances and actuator failures, and uses an adaptive law to approximate model uncertainty. Based on this, a corresponding anti-interference fault-tolerant controller is designed to realize satellite attitude system control, and the satellite control torque is bounded.

[0005] Technical Solution: The present invention provides an active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances. The specific implementation process is as follows:

[0006] (1) Based on the satellite attitude dynamics and kinematic equations, establish a satellite attitude system model that considers external interference, actuator failure and model uncertainty;

[0007] (2) To address the nonlinear external disturbances in the satellite attitude system model, a nonlinear disturbance observer is designed to estimate the external disturbance terms;

[0008] (3) To address the additive actuator faults present in the satellite attitude system model, a fault estimator is designed to estimate the additive actuator faults;

[0009] (4) To address the model uncertainty problem in the satellite attitude system model, an adaptive law is designed to approximate the model uncertainty terms;

[0010] (5) Based on the satellite attitude system model, combined with the observer, estimator, adaptive law and system state, design an anti-interference fault-tolerant controller to realize the attitude control of the satellite; the system state includes the satellite attitude angle and the satellite attitude angular velocity.

[0011] Furthermore, the satellite attitude system model described in step (1) is as follows:

[0012]

[0013] in It is a state variable. , The angles of rotation about axes X, Y, and Z are, in order. This represents the external disturbance torque experienced by the satellite; This indicates an additive fault in the actuator, assuming an actuator failure. and its time derivative For the norm to be bounded; This represents the system's input torque. It is an unknown model uncertainty term, defined as ,matrix Full

[0014] foot , For state variables A bounded function.

[0015] Furthermore, the external disturbance described in step (1) is a nonlinear model, expressed by the following equation:

[0016]

[0017] In the formula, Represents state variables, Indicates external interference. Represents a constant matrix with known dimensions. It is the non-linear part.

[0018] Furthermore, the nonlinear disturbance observer described in step (2) is expressed by the following formula:

[0019]

[0020]

[0021] In the formula, Represents a matrix with a known constant dimension. Represents the state variable, nonlinear part For any constant All meet , This represents the gain of the observer to be designed. It means The estimated value, This represents the system's input torque. This represents an estimated value of the fault.

[0022] Furthermore, the fault estimator described in step (3) is used to estimate actuator faults. To avoid generating high-frequency noise by directly differentiating the state, the system's output information and feedback are used to converge the interference estimation error, thereby deriving the form of the auxiliary intermediate variables and defining the intermediate variables. The description is as follows:

[0023]

[0024] in, This represents an estimated value for the fault. This represents the gain of the observer to be designed, and the fault estimation error is defined as... .

[0025] Furthermore, the adaptive law in step (4) employs an improved algorithm with a continuous-time Lyapunov correction function and a projection operator, expressed as follows:

[0026]

[0027] In the formula, Defined as a continuous-time projection operator. Defined as the continuous-time Lyapunov correction function. It is a given parameter. It is a known matrix. , This represents the estimation error of external disturbances. The estimation error of actuator failure, Indicates the system status.

[0028] Furthermore, the continuous-time projection operator Its form is as follows:

[0029]

[0030] in, It is any positive definite matrix. It is a piecewise continuous time vector and satisfies ; It is a continuously differentiable convex mapping, and for the adaptive law:

[0031]

[0032] in Indicates the system state; if From any initial conditions Departure, fulfillment:

[0033]

[0034] but satisfy:

[0035]

[0036] It can be inferred that if ,but Therefore, the projection operator can guarantee the uniform boundedness of the adaptive law and improve its robustness.

[0037] Furthermore, the continuous-time Lyapunov correction function for:

[0038]

[0039] Among them, parameters And the signal This function is used to prevent the adaptive parameters from drifting. When the error is very small, the adjustment effect of the adaptive law is completely suppressed, preventing unnecessary parameter adjustments when the error is small. When the error is moderate, the adjustment intensity increases linearly with the increase of the error. When the error is large, it adjusts fully to adapt to the larger tracking error.

[0040] Furthermore, the anti-interference fault-tolerant controller mentioned in step (5) is:

[0041]

[0042] In the formula, This indicates the system status. This represents the system's input torque. This represents an estimated value for the fault. This represents an estimated value of the interference. This represents the uncertain approximation value of the model. These are the parameters for the controller to be designed.

[0043] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: The external interference model used in this invention is a nonlinear model, which better reflects the interference experienced by satellites in actual operation; the nonlinear interference observer used in this invention can effectively extract interference features and achieve accurate estimation of dynamic interference, while also possessing stronger real-time performance while meeting accuracy requirements; the adaptive law used in this invention can ensure accurate approximation of the uncertainty of the unknown model while the estimated parameters are bounded, and this adaptive law can effectively avoid parameter drift, ensuring that the estimated parameters are always stable and reliable; the anti-interference fault-tolerant controller used in this invention introduces the system state, external interference estimation compensation term, fault compensation term, and adaptive compensation term into the control law, which enhances the ability to suppress multiple factors and strengthens the robustness of the system. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the process of the present invention;

[0045] Figure 2 This is a schematic diagram illustrating the principle of the active fault-tolerant control method for satellite attitude systems proposed in this invention.

[0046] Figure 3 This is a graph showing the interference estimation error results under the condition of external disturbance torque;

[0047] Figure 4 This is a graph showing the fault estimation error results in the presence of actuator failure.

[0048] Figure 5 This is a graph showing the results of the uncertain approximation error under the condition of model uncertainty;

[0049] Figure 6 This is a graph showing the satellite's attitude angles.

[0050] Figure 7 This is a graph showing the satellite's attitude and angular velocity.

[0051] Figure 8 The graph shows the variation of the satellite control torque input. Detailed Implementation

[0052] The invention will now be further described with reference to the accompanying drawings.

[0053] like Figure 1As shown, this invention proposes an active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances. By introducing modelable external nonlinear disturbances, a mathematical model of the satellite attitude system is established considering factors such as external disturbances, actuator failures, and model uncertainties. Furthermore, a disturbance observer is designed to estimate external disturbances in real time, while a fault estimator dynamically estimates actuator failures. An adaptive law is constructed to approximate the uncertainty of the system model. Finally, a joint design scheme for the observer, estimator, adaptive law, and control law is presented, enabling the satellite to maintain asymptotic stability under the influence of multiple factors. Specifically, the method includes the following steps:

[0054] Step 1: Based on the satellite attitude dynamics and kinematic equations, establish a mathematical model of the satellite attitude system that considers external interference, actuator failure, and model uncertainty.

[0055] Taking micro- and nano-satellites as the research object, a mathematical model of the satellite attitude system is established. Since the Euler angle representation method can achieve convenient geometric understanding and implementation through intuitive rotation sequences, this invention uses Euler angles to describe the satellite's attitude dynamics equations.

[0056] Euler angles: Euler angles define three rotations about the coordinate axes. There are several common orders, such as... ,for In order, the rotation matrix is ​​the product of the three fundamental rotation matrices:

[0057]

[0058] in, It is around Axis rotation , It is around Axis rotation , It is around Axis rotation These basic matrices are as follows:

[0059]

[0060] The attitude matrix represented by Euler angles is related to the choice of rotation order. The transformation matrix corresponding to the order is represented as follows:

[0061]

[0062] The rotation of a satellite can be achieved using Euler angles. To describe it. Euler angles are a commonly used method for attitude description. In the attitude description of a three-dimensional rigid body, Euler angles achieve spatial positioning through the combination of three rotation axes. There are three commonly used definitions of Euler angles. This invention uses the ZXY rotation sequence. Euler angles decompose rotation into rotations in three directions. Assuming the rotation angles X, Y, and Z around the axes are respectively... Then we can obtain the satellite attitude kinematic equations:

[0063]

[0064] in:

[0065]

[0066] According to Newton's Euler equations

[0067]

[0068]

[0069]

[0070] The derived equations for satellite attitude dynamics are as follows:

[0071]

[0072] in, This represents the satellite's moment of inertia matrix. This represents the torque acting on the satellite. This represents the satellite's angular velocity, expressed as follows:

[0073]

[0074] Further transformation, considering multiple factors such as external interference, actuator failure, and model uncertainty, establishes the following mathematical model for the satellite attitude system:

[0075]

[0076] in It is a state variable. ,in The angles are, in order, the rotations around axes X, Y, and Z. This represents the external disturbance torque experienced by the satellite. This indicates an additive fault in the actuator, assuming an actuator failure. and its time derivative It is a norm-bounded function. This represents the system's input torque. It is an unknown model uncertainty term, defined as ,matrix

[0077] satisfy ,in For state variables A bounded function.

[0078] External disturbances can be described by the following nonlinear model:

[0079]

[0080] in, Let w(t) be a constant matrix of known dimension, representing the state variables and the nonlinear part. For any constant All meet In some cases, describing satellite interference using a linear system may lead to modeling uncertainties. Extending the interference represented by a linear system to a nonlinear system makes the interference more consistent with reality. Therefore, the modelable nonlinear external interference used in this invention is more consistent with the interference experienced by satellites in actual operation.

[0081] Step 2: Based on the satellite attitude system model, design a nonlinear interference observer to estimate the external interference term.

[0082] like Figure 2 As shown, based on the characteristics of external interference, in order to effectively extract interference features and achieve real-time estimation of dynamic interference, a nonlinear interference observer is designed to estimate external interference, using the original nonlinear interference model as a foundation.

[0083] By introducing auxiliary variables, adding observer gain for feedback correction, and combining this with real-time changes in the satellite system's state for dynamic updates, real-time interference updates are ultimately achieved; described as follows:

[0084]

[0085]

[0086] in, This represents the gain of the observer to be designed. It means The estimated value is used to finally obtain the estimated value of external disturbance. The estimation error of external disturbances is defined as follows: .

[0087] Step 3: Based on the satellite attitude system model, design a fault estimator to estimate additive faults in the actuators.

[0088] A fault estimator is designed to estimate actuator faults. To avoid high-frequency noise generated by directly differentiating the state, the system's output information and feedback are used to converge the interference estimation error, thus deriving the form of the auxiliary intermediate variables. The intermediate variables are defined. The description is as follows:

[0089]

[0090] in This represents an estimated value for the fault. This represents the gain of the observer to be designed, and the fault estimation error is defined as... .

[0091] Step 4: Based on the satellite attitude system model, design an adaptive law to approximate the model's uncertainties. For example... Figure 2 As shown, to effectively avoid parameter drift, this paper adopts an improved adaptive algorithm with a continuous-time Lyapunov correction function and projection operator:

[0092]

[0093] Here, the continuous-time projection operator is defined. Its form is as follows:

[0094]

[0095] in, It is any positive definite matrix. It is a piecewise continuous time vector and satisfies . It is a continuously differentiable convex mapping, for the adaptive law , Indicates the system status. If... From any initial conditions Departure, fulfillment:

[0096]

[0097] but satisfy:

[0098]

[0099] It can be inferred that if ,but Therefore, the projection operator can guarantee the uniform boundedness of the adaptive law and improve its robustness.

[0100] The Lyapunov correction function, defined as a continuous-time function, has the following form:

[0101]

[0102] Among them, parameters And the signal This function is used to prevent adaptive parameter drift. When the error is small, the adaptive law's adjustment is completely suppressed, preventing unnecessary parameter adjustments with small errors. When the error is moderate, the adjustment increases linearly, with the strength of the adjustment increasing linearly with the increase of the error. When the error is large, it adjusts fully to adapt to the larger tracking error. This adaptive law effectively avoids parameter drift, ensuring that the estimated parameters remain stable and reliable.

[0103] Step 5: Based on the satellite attitude system model, and combining the observer, estimator, adaptive law, and system state (satellite attitude angle and satellite attitude angular velocity), design an anti-interference fault-tolerant controller to realize the attitude control of the micro-nano satellite.

[0104] For satellite attitude control systems facing external disturbances, actuator failures, and modeling uncertainties, a fault-tolerant controller is proposed. Combining an observer, estimator, adaptive law, and system state, this controller aims to ensure system stability. It effectively copes with the influence of the aforementioned disturbances, as described below:

[0105]

[0106] in, This indicates the system status. This represents an estimate of external disturbances. This represents an estimated value for the fault. This represents the approximate value that is uncertain in the model.

[0107] Define the estimation error of external disturbances Fault estimation error Finally, the system state, external disturbance estimation error, and fault estimation error are obtained as follows:

[0108]

[0109] in, The derivative of the external disturbance estimation error. The derivative of the actuator fault estimation error. It is the approximation error of the uncertain part of the model.

[0110] In this embodiment, the asymptotic stability of the final satellite attitude control system is proved using the Lyapunov function. The Lyapunov function is constructed as follows:

[0111]

[0112] in,

[0113]

[0114] here It is a positive definite symmetric matrix with appropriate dimensions. Taking the derivative of this Lyapunov function, we get:

[0115]

[0116] For any External interference has the following characteristics:

[0117]

[0118] Due to signal It is energy-bounded, for the existence of positive scalars. , Introduction Performance metrics are used to suppress its impact, i.e., the following conditions must be met:

[0119]

[0120] Suppose there exists a parameter matrix satisfy Thus, it is possible to obtain Assuming given parameters There exists a known matrix , making It is a positive definite matrix, that is Therefore, we can obtain Utilizing properties We can obtain:

[0121]

[0122]

[0123]

[0124] because ,therefore The following inequalities must be satisfied:

[0125]

[0126] The projection operator, as defined, has the following properties:

[0127]

[0128] Among them, parameters express The estimated value is obtained, thus yielding The projection operator for a matrix is ​​expressed as follows:

[0129]

[0130] in, Therefore, the projection operator has the following properties:

[0131]

[0132] In the formula, ,parameter express The estimated value.

[0133] Therefore, we can conclude that:

[0134]

[0135] By combining linear matrix inequalities and considering the characteristics of external disturbances, actuator fault terms, and model uncertainties, the following sufficient conditions are obtained to make the satellite attitude system asymptotically stable.

[0136]

[0137] The expressions for the elements in the LMI above are as follows:

[0138]

[0139] in For a positive definite matrix of appropriate dimension, And it is a scalar. Because the system model contains nonlinear terms, such as... Therefore, the gain of the controller Observer gain and the gain of the estimator Since the problem cannot be directly solved using the Matlab toolbox, a matrix transformation is used to treat the nonlinear terms, transforming them into linear constraints. This converts the problem into a standard optimization problem, leading to the development of an optimization framework based on linear matrix inequalities. This framework can simultaneously solve for the gain parameters of the observer, estimator, and controller. The sufficient condition for the asymptotic stability of the satellite attitude system is finally transformed into:

[0140]

[0141] in,

[0142]

[0143] If there exists a positive definite matrix of appropriate dimension constant matrix and scalar If the following LMI holds, then the closed-loop system is stable, meaning the satellite attitude control system achieves the desired control objective. Here, the controller gain, disturbance observer gain, and fault estimator gain are respectively expressed as follows:

[0144]

[0145] The anti-interference fault-tolerant controller proposed in this invention was simulated and verified in MATLAB. The selected satellite was a microsatellite, and the relevant satellite parameters were set as follows:

[0146] Considering the satellite's moment of inertia:

[0147]

[0148] The satellite's initial attitude angle is The initial angular velocity is 0.01. .

[0149] The model parameters for the externally modelable disturbance system are selected as follows:

[0150]

[0151] Nonlinear terms Meanwhile, the actuator fault items are:

[0152]

[0153] The parameters for the uncertain parts of the model are selected as follows:

[0154]

[0155] The model uncertainty term is selected as follows:

[0156]

[0157] in Represented as:

[0158]

[0159] Regarding state variables Bounded functions Represented as:

[0160]

[0161] Where the function The relevant parameters are selected as follows ,function The relevant parameters are selected as follows .

[0162] Select the appropriate parameters This paper implements the numerical solution process using the LMI toolbox in Matlab, which allows us to obtain the observer gain. Estimator gain Fault-tolerant controller gain as follows:

[0163]

[0164] This invention proposes a design method for a nonlinear disturbance observer, a fault estimator, an adaptive law, and an anti-interference fault-tolerant controller. If all four systems satisfy the asymptotic stability condition, it indicates that external disturbances and actuator faults have been effectively estimated, model uncertainties have been effectively approximated, the controller has achieved the preset performance, the stability of the satellite system has been ensured, and the final control objective has been achieved.

[0165] Figure 3 , Figure 4 and Figure 5 The figures represent the changes in external disturbance estimation error, fault estimation error, and model uncertainty approximation error over time under the conditions of external disturbance torque, actuator failure, and model uncertainty, respectively. They show that the errors converge rapidly to zero and remain stable over time. The simulation experiment verifies the accuracy and effectiveness of the design. Figure 6 and Figure 7 The actual position and angular velocity of the system are shown respectively, indicating that the system state is asymptotically stable when the estimation errors of the disturbance observer and fault estimator and the uncertain approximation error converge. This verifies the effectiveness and accuracy of the joint design scheme of observer, estimator, adaptive law and controller. Figure 8 The changes in satellite control torque input throughout the entire satellite attitude control process are shown, which conform to actual conditions and remain within an effective range. This demonstrates the rationality and effectiveness of the controller, interference observer, fault estimator, and adaptive law designed in this invention. In summary, the anti-interference fault-tolerant controller adopted in this invention can enable the satellite's state to converge rapidly and maintain stability when facing multiple interference factors, thus achieving attitude control of the satellite under multiple interference factors.

[0166] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for active fault-tolerant control of a satellite attitude system based on an observer under dynamic disturbances, characterized in that, Includes the following steps: (1) Based on the satellite attitude dynamics and kinematic equations, establish a satellite attitude system model that considers external interference, actuator failure and model uncertainty; (2) To address the nonlinear external disturbances in the satellite attitude system model, a nonlinear disturbance observer is designed to estimate the external disturbance terms; (3) To address the additive actuator faults present in the satellite attitude system model, a fault estimator is designed to estimate the additive actuator faults; (4) To address the model uncertainty problem in the satellite attitude system model, an adaptive law is designed to approximate the model uncertainty terms; (5) Based on the satellite attitude system model, combined with the observer, estimator, adaptive law and system state, design an anti-interference fault-tolerant controller to realize the attitude control of the satellite.

2. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 1, characterized in that, The satellite attitude system model mentioned in step (1) is as follows: ； in It is a state variable. , The angles of rotation about axes X, Y, and Z are, in order. This represents the external disturbance torque experienced by the satellite; This indicates an additive fault in the actuator, assuming an actuator failure. and its time derivative For norm bounded; This represents the system's input torque. It is an unknown model uncertainty term, defined as ,matrix Full foot , For state variables A bounded function.

3. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 1, characterized in that, The external disturbance mentioned in step (1) is a nonlinear model, expressed by the following formula: ； In the formula, Represents state variables, Indicates external interference. Represents a constant matrix with known dimensions. It is the non-linear part.

4. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 1, characterized in that, The nonlinear disturbance observer described in step (2) is expressed by the following formula: ； ； In the formula, Represents a constant matrix with known dimensions. Represents the state variable, nonlinear part For any constant All meet , This represents the gain of the observer to be designed. It means The estimated value, This represents the system's input torque. This represents an estimated value of the fault.

5. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 1, characterized in that, The fault estimator described in step (3) is used to estimate actuator faults. To avoid high-frequency noise generated by directly differentiating the state, the system's output information and feedback are used to converge the interference estimation error, and the form of the auxiliary intermediate variables is derived. The intermediate variables are then defined. The description is as follows: ； in, This represents an estimated value for the fault. This represents the gain of the observer to be designed, and the fault estimation error is defined as... .

6. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 1, characterized in that, The adaptive law in step (4) employs an improved algorithm using a Lyapunov correction function with continuous time and a projection operator, expressed as follows: ； In the formula, Defined as a continuous-time projection operator. Defined as the continuous-time Lyapunov correction function. It is a given parameter. It is a known matrix. , This represents the estimation error of external disturbances. The estimation error of actuator failure, Indicates the system status.

7. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 6, characterized in that, The continuous-time projection operator Its form is as follows: ； in, It is any positive definite matrix. It is a piecewise continuous time vector and satisfies ; It is a continuously differentiable convex mapping, and for the adaptive law: ； in Indicates the system state; if From any initial conditions Departure, fulfillment: ； but satisfy: ； Infer if ,but Therefore, the projection operator can guarantee the uniform boundedness of the adaptive law and improve its robustness.

8. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances as described in claim 6, characterized in that, The continuous-time Lyapunov correction function for: ； Among them, parameters And the signal This function is used to prevent the adaptive parameters from drifting. When the error is very small, the adjustment effect of the adaptive law is completely suppressed, preventing unnecessary parameter adjustments when the error is small. When the error is moderate, the adjustment intensity increases linearly with the increase of the error. When the error is large, it adjusts fully to adapt to the larger tracking error.

9. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances according to claim 1, characterized in that, The anti-interference fault-tolerant controller mentioned in step (5) is: ； In the formula, This indicates the system status. This represents the system's input torque. This represents an estimated value for the fault. This represents an estimated value of the interference. This represents the uncertain approximation value of the model. These are the parameters for the controller to be designed.

10. The active fault-tolerant control method for a satellite attitude system based on an observer under dynamic disturbances according to claim 1, characterized in that, The system state described in step (5) includes the satellite's attitude angle and the satellite's attitude angular velocity.

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